Truth tables are an extremely inefficient method for checking the validity of a logical argument. Proofs are less algorithmic but are much faster to complete.

**Takeaway Points**

- Proofs begin with premises. In homework assignments, you will usually be given a conclusion that you need to find using those premises.
- You may use rules of replacement or inference on any line above the current line.
- All lines must cite their reasoning.
- The last line should be what you are trying to prove.
- Proofs in academic work are much harder because you often have to prove individual premises on your own and you are often unsure what you are trying to prove.